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Residue theorem and incomplete Gamma functions

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#improper-integrals #gamma-function #residue-calculus
178
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Higher order factorials.

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#functions #factorial #gamma-function
92
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How to find $\Gamma(i)$?

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#complex-numbers #gamma-function
60
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Can anyone tell me the name of this function?

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#analysis #special-functions #gamma-function #riemann-zeta #statistical-mechanics
232
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Sufficient statistics for beta-binomial distribution

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#statistics #special-functions #gamma-function #beta-function
178
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Use the $\Gamma$ function to solve $\int_{-\infty}^{\infty} e^{xt - e^{t}} dt$

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#calculus #integration #special-functions #gamma-function
140
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Taylor series of $\sum_{k=0}^\infty \frac{x^k}{k!} \log(\Gamma(k+1))$

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#power-series #gamma-function
1k
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Simplify $\Gamma\left(\frac27\right) \Gamma\left(\frac{11}{42}\right)/\;\Gamma\left(\frac1{21}\right)$ to elementary terms

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#calculus #trigonometry #special-functions #gamma-function
623
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Showing that $\Gamma(x)\Gamma(y) = \Gamma(x+y)\beta(x,y)$ via change of variable

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#special-functions #gamma-function #beta-function
178
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How to derive the domain of Gamma function

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#gamma-function #gamma-distribution
261
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Gamma Identities from Inverse Transform

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#gamma-function #inverse-function #hypergeometric-function #mellin-transform
226
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Manipulation of gamma functions

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#gamma-function
202
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Approximating Log(Gamma(z)) for small z as Log(Gamma(z + 1)) - Log(z)

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#numerical-methods #gamma-function #approximation-theory
267
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Proof that Integral over the arc vanishes as $R\rightarrow\infty$ in Inverse Mellin Transform of $\Gamma(s)$

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#integration #limits #contour-integration #gamma-function #mellin-transform
51
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Show that $B(\alpha,\alpha)=2\int_0^{\frac{1}{2}}(\frac{1}{4}-(\frac{1}{2}-x)^{2})^{\alpha-1}dx$

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#gamma-function #beta-function

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